Given any pair of positive densities \(\pi , \eta \)  on \(\mathbb {R}^n\) , there exists a
unique monotone triangular transport map \(S\) —called the
Knothe–Rosenblatt (KR) rearrangement—that
pushes forward one of the corresponding distributions to the other [1]}, i.e., if \(Z\sim \pi \) , then
\(S(Z)\sim \eta \) .
A (lower) triangular map \(S:\mathbb {R}^n\rightarrow \mathbb {R}^n\)  is a multivariate
function whose \(k\) th component, \(S^k\) , depends only on the first \(k\)  input variables, i.e.,
\(S( z) = \left[\begin{array}{l}S^1(z_1)\\[2pt]S^2(z_1,z_2)\\\vdots \\S^n(z_1,z_2,\dots z_n)\end{array}\right].\) 
